1. Apr 22, 2015

### Strange design

Is it correct to say that two arbitrary charged particles in space have a spacetime separation of zero? And if so, is this the explanation for how the electrostatic force between them acts instantaneously across any 3 dimensional distance. (By "instantaneously" I mean that the force would appear the instant that the particles do)

Pardon me if the question isn't posed properly, or if it's completely absurd. As mentioned above, I'm new to relativity.

2. Apr 22, 2015

### Mentz114

What do you mean by 'spacetime separation' ? I also doubt if any influence, including an electric field can travel instantaneously. That is one of the no-nos of special relativity.

Of course, charges cannot just appear out of nowhere so the question is somewhat ill-posed.

Where did you get these ideas? ( I'm being curious, not critical, here)

http://physics.stackexchange.com/questions/93390/field-of-moving-charge-lorentzlienard-wiechert

Last edited: Apr 22, 2015
3. Apr 22, 2015

### Strange design

Well, what I wrote was my paraphrasing of what I interpreted that my professor was saying in lecture. He was posing how relativity explained the "action at a distance," of the gravitational and electrostatic forces. I may have misinterpreted what he said.

I certainly didn't mean to suggest the creation of new charge in my question. I meant more on the lines of say, a neutral atom emitting an electron on one side of the universe, and another atom doing the same on the other side of the universe. Would those two electrons not have an instant electrostatic force between them, regardless of their distance in 3 dimensions? (Obviously the size of the force is irrelevant)

Are you saying then that electric fields propagate at the speed of light?

4. Apr 22, 2015

### Staff: Mentor

No.

It doesn't. But if all you look at is the electrostatic force, you won't see how the force propagates. An electrostatic force, by definition, is static: nothing changes. That means nothing propagates; you have basically adopted an approximation where the force a charged object will experience at any point in space is already predetermined, and in this approximation the concept of "speed of propagation" of a force makes no sense.

In order to see propagation, you have to look at electrodynamics: what happens when things change. See below.

No. If the two electrons are a billion light-years apart when they are created, then it will take a billion years for either one to feel any force from the other. This is because you are now including a change: a charged particle is produced where there was none before. (Strictly speaking, of course, charge is conserved; the neutron decay doesn't just produce an electron, it also produces a proton--and a neutrino, but the neutrino is uncharged. But we can assume, for purposes of a thought experiment, that the proton flies off in the opposite direction very quickly, so we can ignore its charge when looking at the electron-electron interaction. Or we could have the electron fly off, since it's a lot lighter, and look at the interaction between the two protons.) Thus, there is a change in the source of the EM field, which means the electrostatic equations do not apply; you have to use the more general equations that cover dynamic situations.

Yes. The electrodynamic equations--Maxwell's Equations--tell you that, whenever there is a change in the source of the field, an electromagnetic wave is created that carries information about the change--the change in the field produced by the change in the source. This wave propagates at the speed of light.

5. Apr 22, 2015

### Strange design

Thanks for taking the time to explain that. I thought what he was articulating was that because the field is propagating at the speed of light, the time dilation would mean that from the "field's frame of reference" it would arrive instantaneously. I realize that you can't take the frame of reference of a field or a photon because you can't have a velocity of 0 and C simultaneously, but I surmised that he was saying from the "fields perspective" it essentially would be in all places instantly because for "it" delta t would go to zero.
Again, I may have totally misinterpreted what he was saying, and again, I thank you for taking the time to help me dissect what I thought I heard.

6. Apr 22, 2015

### Strange design

Thanks for the link. In the answer posted there, the writer calls it the "instantaneous field." What is meant by that?

7. Apr 22, 2015

### Mentz114

It means 'at a particular instant in time'. If you wait longer than an instant - it has changed.

I think PeterDonis has given the definitive answer.

8. Apr 22, 2015

### Staff: Mentor

This is not correct, and it's a good illustration of why it's misleading to say that "time stops" at the speed of light, or words to that effect. Unfortunately, many sources are sloppy about this and either don't realize or don't care that the language they use is inviting incorrect inferences.